Vortex dynamics in a temperature gradient

The motion of vortices in a type II superconductor leads to a heat current, which has two main contributions in the hydrodynamic regime: one is due to the heat carried by the vortices themselves and leads to transverse thermomagnetic effects such as the Nernst and Ettingshausen effects. The second contribution is of comparable magnitude and perpendicular to the direction of vortex motion. It arises from what is called the spectral flow effect, which couples the motion of vortices to that of the normal fluid. The existence of this coupling simultaneously explains the small Hall angle and the occurance of longitudinal thermomagnetic effects like the thermopower and the Peltier effect. We briefly summarize the experimental results on thermomagnetic effects in superconductors. We discuss the origin of the two contributions to the heat current and present an analysis of vortex motion in a temperature gradient. We derive in particular an equation of motion for a vortex in a temperature gradient. Our analysis of vortex motion is in excellent agreement with experimental results. (orig.)